If the curves, $x^{2}-6 x+y^{2}+8=0$ and $\mathrm{x}^{2}-8 \mathrm{y}+\mathrm{y}^{2}+16-\mathrm{k}=0,(\mathrm{k}>0)$ touch each other at a point, then the largest value of $\mathrm{k}$ is

The gradient of the radical axis of the circles ${x^2} + {y^2} - 3x - 4y + 5 = 0$ and $3{x^2} + 3{y^2} - 7x + 8y + 11 = 0$ is

Three circles of radii $a, b, c\, ( a < b < c )$ touch each other externally. If they have $x -$ axis as a common tangent, then

The circles $x^2 + y^2 + 2x -2y + 1 = 0$ and $x^2 + y^2 -2x -2y + 1 = 0$ touch each  other :-

$P, Q$ and $R$ are the centres and ${r_1},\,\,{r_2},\,\,{r_3}$ are the radii respectively of three co-axial circles, then $QRr_1^2 + RP\,r_2^2 + PQr_3^2$ is equal to

If the equation of the common tangent at the point $(1, -1)$ to the two circles, each of radius $13$, is $12x + 5y -7 = 0$, then the centre of the two circles are